Calc II Partial Fractions with Natural Logs

[demersal]

Homework Statement

$$\int$$$$\frac{dx}{x(1+ln x)}$$

Homework Equations

Partial Fractions? Maybe I am solving this wrong...

The Attempt at a Solution

$$\frac{A}{X}$$ + $$\frac{B}{1+ln x}$$ = 1

A(1+lnx) + Bx =1
A + Alnx + Bx =1

This doesn't seem to work out properly. I have been having a lot of trouble understanding partial fractions so any help in assisting me in making this first step of the problem would be greatly appreciated! Even if partial fractions aren't the correct way to go about this, if you could explain how you knew what to do, I think it would help me a lot in the long run! Thanks!

 

[danago]

I don't think you can use partial fractions like that since the integrand is not a rational function.

Try a substitution, let u=1+ln x

 

[rocomath]

let u=lnx

 

[rocomath]

ignore me! i was sick :(

 

[danago]

ignore me! i was sick :(

Your sub still works too